Large Avalanche Turn Outward Problem

The problem  

Jonathan Cano: White made a mistake in the large avalanche joseki . White reinforces with , and then tries to fight it out on the top.

One possible continuation.  

Jonathan Cano:I've looked at some variations that begin with Black a followed by Black b but I don't feel I could play Black here and be certain of killing one of the and groups ...

A solution? (Black 11 at 'a')  

Andre Engels: After , if White plays at here, Black captures the top group. After Black 11, Black clearly has one liberty more.

Does not work either (Black 11 at 'a')  

If instead White plays hane at like here, Black seems to be capturing white stones somewhere, after which the group is dead as well.

Also not interesting  

White might try playing here to live, but even if it works, she needs to add a second stone almost immediately, and the white stones at the right seem to be heading for a fall.

Jonathan Cano: Thanks Andre!

Large avalanche, Black turns outside  

Jonathan Cano: the normal move for White here is a. In Dictionary of Basic Joseki Ishida Yoshio says at b is a mistake.

A mistake by White  

Jonathan Cano: Ishida says " seems vulgar but it avoids complications and guarantees a favorable result. For his part White has no choice but to make the vulgar ataris of and . White answers at a or b."

A mistake by White, continuation b.1  

Jonathan Cano: Here is the continuation when White plays at b in the diagram above.

A mistake by White, continuation b.3  

Jonathan Cano: After Black 2 Ishida says Black a and b are miai so White is hopeless.

How professionals play  

Checking MasterGo, I found that professionals actually play (4 games out of 4) here rather than at as Ishida proposes. After , Black plays either a or b, after which the various groups in the diagram fight things out.